Problem: What's the first wrong statement in the proof below that $ \triangle CEF \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{AC} \cong \overline{CE}$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ $ \overline{BD} \cong \overline{CF}$ $, \ $ $ \angle DBE \cong \angle CFE$ $, \ $ and $\ $ $ \angle BED \cong \angle CEF$ Proof $ \triangle CEF \cong \triangle CAB$ because AAS $ \overline{CF} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \triangle DEB \cong \triangle CAB$ because AAS $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \triangle CAB \cong \triangle CEB$ because SSS $ \triangle CEF \cong \triangle CEB$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle CAB \cong \triangle DEB$ is the first wrong statement.